Related papers: Entropy and Convexity for Nonlinear Partial Differ…
A simple expression for the non-equilibrium distribution function in ultra-fast transient processes is proposed. Postulating its dependence on temporal derivatives of the equilibrium integrals of motion, non-equilibrium analogues of the…
Several results of black holes thermodynamics can be considered as firmly founded and formulated in a very general manner. From this starting point we analyse in which way these results may give us the opportunity to gain a better…
We combine the formalisms of diagonal entropy and Jarzynski Equality to study the thermodynamic properties of closed quantum systems. Applying this approach to a quantum harmonic oscillator, the diagonal entropy offers a notion of…
The time variation of entropy, as an alternative to the variance, is proposed as a measure of the diffusion rate. It is shown that for linear and time-translationally invariant systems having a large-time limit for the density, at large…
Through the consideration of spherically symmetric gravitating systems consisting of perfect fluids with linear equation of state constrained to be in a finite volume, an account is given of the properties of entropy at conditions in which…
The physical meaning of entropy is analyzed in the context of statistical, nuclear, atomic physics and cosmology. Only the microcanonical Boltzmann entropy leads to no contradictions in several simple, elementary and for thermodynamics…
Controversy exists regarding the possible existence of a transition between the liquid and glassy states of water. Here we use experimental measurements of the entropy, specific heat, and enthalpy of both liquid and glassy water to…
The displacement $\lambda$-convexity of a nonstandard entropy with respect to a nonlocal transportation metric in finite state spaces is shown using a gradient flow approach. The constant $\lambda$ is computed explicitly in terms of a…
Thermodynamics allows the application of Statistical Mechanics to finite and even small systems. As surface effects cannot be scaled away, one has to be careful with the standard arguments of splitting a system into two or bringing two…
Entropy production is a fundamental concept that plays a crucial role in the second law of thermodynamics and the measure of irreversibility. It imposes rigorous constraints on the kinds of transformations allowed in thermodynamic…
Partial differential equations (PDEs) describing thermodynamically isolated systems typically possess conserved quantities (like mass, momentum, and energy) and dissipated quantities (like entropy). Preserving these conservation and…
In these decades, it has been revealed that there is rich information-theoretic structure in thermodynamics of out-of-equilibrium systems in both the classical and quantum regimes. This has led to the fruitful interplay among statistical…
The time decay of fully discrete finite-volume approximations of porous-medium and fast-diffusion equations with Neumann or periodic boundary conditions is proved in the entropy sense. The algebraic or exponential decay rates are computed…
The state function entropy and its quantum thermodynamical implication for two typical dissipative systems with anomalous spectral densities are studied by investigating on their low-temperature quantum behavior. In all cases it is found…
We numerically determine the entropy for heat-conducting states, which is connected to the so-called excess heat considered as a basic quantity for steady-state thermodynamics in nonequilibrium. We adopt an efficient method to estimate the…
We consider degenerate diffusion equations of the form $\partial_tp_t = \Delta f(p_t)$ on a bounded domain and subject to no-flux boundary conditions, for a class of nonlinearities $f$ that includes the porous medium equation. We derive for…
*First-principles derivation of the entropy production in erectric static conduction. *The second-order (symmetric) density matrix contributes to the entropy production. *New schemes of steady states formulated using a relaxation-type von…
It exists a large class of systems for which the traditional notion of extensivity breaks down. From experimental examples we induce two general hypothesis concerning such systems. In the first the existence of an internal coordinate system…
Among various possible routes to extend entropy and thermodynamics to nonequilibrium steady states (NESS), we take the one which is guided by operational thermodynamics and the Clausius relation. In our previous study, we derived the…
Information dynamics is an emerging description of information processing in complex systems which describes systems in terms of intrinsic computation, identifying computational primitives of information storage and transfer. In this paper…